(6x+1)(4x-6)=180

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Solution for (6x+1)(4x-6)=180 equation:



(6x+1)(4x-6)=180
We move all terms to the left:
(6x+1)(4x-6)-(180)=0
We multiply parentheses ..
(+24x^2-36x+4x-6)-180=0
We get rid of parentheses
24x^2-36x+4x-6-180=0
We add all the numbers together, and all the variables
24x^2-32x-186=0
a = 24; b = -32; c = -186;
Δ = b2-4ac
Δ = -322-4·24·(-186)
Δ = 18880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{18880}=\sqrt{64*295}=\sqrt{64}*\sqrt{295}=8\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{295}}{2*24}=\frac{32-8\sqrt{295}}{48} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{295}}{2*24}=\frac{32+8\sqrt{295}}{48} $

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